Classical asymmetric cryptographic algorithms used in the field of security for electronic communications and in particular network scaling, authentication and identity management, detection, revocation and encryption methods, intrusion detection, signature, non-repudiation, authorization, digital rights management, provenance and key related network security functions may be broken with quantum computers, as there may exist several processes being executed at the same time.
Existing authentication methods, such as the so-called RSA cryptosystem introduced by Rivest, Shamir and Adleman in 1977, ECC (Elliptic Curve Cryptography), or the like, are either not resistant against quantum computer attacks, or require large key sizes, such as, e.g., with methods like the McEliece method introduced by McEliece in 1978, or Rainbow table method, which employs a precomputed table for reversing cryptographic hash functions.
There exist a few alternative post-quantum cryptography methods, but they all require a large number of key bits. The best known methods, like SIDH (supersingular isogeny Diffie-Hellman key exchange) and NTRU (an open source public-key cryptosystem using lattice based cryptography to encrypt and decrypt data), require around 6000 key bits for 128 bits of security.
Variants of the known Shor's Algorithm for factorization and discrete logarithms allow quantum computers to break existing authentication methods. Post quantum cryptography methods exist that are not broken by variants of Shor's Algorithm, but they require large key and/or signature lengths and high computational effort.
Cryptographic algorithms and authentication schemes usually are based on generated pseudo random numbers. According to prior art, e.g., a one directional chain of hash values may be used as pseudo random number generator comprising a counter as an offset for choosing random number selection. Thus the counter is part of the key and increases key size.
Hash functions are components for many important information security applications, including the generation and verification of digital signatures, key derivation, and pseudo random bit generation.
A hash function is a function on binary data (i.e., bit strings) for which the length of the output is fixed. The input to a hash function is called the message, and the output is called the (message) digest or hash value. The digest often serves as a condensed representation of the message. The so-called SHA-3 family of hash functions according to state of the art consists of four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384, and SHA3-512; in each case, the suffix after the dash indicates the fixed length of the digest, e.g., SHA3-256 produces 256-bit digests.